CAIRO — Islamist militants shot down an Egyptian military helicopter in the Sinai Peninsula with a surface-to-air missile over the weekend, raising new alarms about the terrorist insurgency that developed there in response to the military takeover last summer.

The attack — described by witnesses, documented in a video released by the militants, and confirmed by three people briefed on the Egyptian government’s investigation — validated longstanding fears that such weapons would spill into Egypt and beyond after the Libyan civil war tore open Col. Muammar el-Qaddafi’s fearsome arsenals.

Known as manpads, for man-portable air defense systems, the missiles can bring down commercial airliners if they are flying at low altitude, as during takeoff and landing. They also strengthen Sinai-based militants’ hand against the Egyptian Army, and there is